Short answers, pulled from the story.
Operation Sledgehammer was an Allied plan for a cross-Channel invasion of France in 1942, intended to relieve pressure on the Soviet Red Army by establishing a second front. It called for seizing the French Atlantic ports of Brest or Cherbourg and areas of the Cotentin Peninsula in the autumn of 1942, then building up forces for a spring 1943 breakout.
The British rejected Sledgehammer as premature and impractical, citing the likely scale of German resistance. Because American troops were not yet available in sufficient numbers, British forces would have borne the primary burden, and British officials did not believe the plan was feasible.
Operation Torch, the Allied invasion of French North Africa, replaced Sledgehammer. It launched in November 1942 after President Roosevelt issued a direct order giving Torch precedence over all other operations.
The United States military, including General George C. Marshall, and the Soviet Union, including Foreign Minister Vyacheslav Molotov, pressed for Sledgehammer. The British rejected it, arguing a 1942 landing in France was premature.
Roosevelt issued his direct order after the Combined Chiefs of Staff met in London on the 30th of July 1942, following the Second Claridge Conference held from the 20th to the 26th of July. It was one of only two direct orders he gave to military commanders during the war.
Operation Roundup was the original Allied plan for invading continental Europe before April 1943, using 48 divisions, 18 of them British. Sledgehammer was a contingency alternative, targeting 1942 rather than 1943, designed to open a second front sooner if the situation on the Eastern Front demanded it.